It is well-known that signal processing systems using digital or two-state signals (i.e. those that have only two amplitude levels) have numerous advantages over systems using continuous signals. Two-state signals are less sensitive to variations in the operating characteristics of the electronic devices making up the system because all that is important is the discrimination between the two amplitude levels. It is therefore also not necessary that the devices operate linearly. Also, since the active circuit elements can be operated in a switching mode, which consumes less power than a continuous mode, digital systems are inherently more efficient than purely analog systems.
One common signal processing application to which digital techniques have been applied is that of amplification. Audio power amplifiers for automobile sound systems, where efficiency is a very important consideration, are particularly suitable for the application of digital techniques.
Shown in FIG. 1 is a basic schematic of a type of two-state or switching amplifier well known to the art. (In all the following descriptions, each designation of electrical components such as resistors or capacitors will be taken to refer both to the component and to its value.) The inverting input terminal of comparator U1 is connected to ground through capacitor C.sub.1, and to the U1 output terminal via negative feedback resistor R.sub.f. The voltage applied to the inverting terminal is designated V.sub.c and to the noninverting terminal Vp. The noninverting input terminal is connect to ground via resistor R.sub.1 and to the U1 output terminal by resistor R.sub.2. An input signal V.sub.i is applied to the inverting input of U1, a signal Vo appears at the U1 output. R.sub.3 is made very large so as to isolate the amplifier input from the input signal source. The operation of the amplifier is as follows. Assume that U1 is connected to a power supply such that its output swings between -10 and +10 volts, depending upon whether the voltage difference between its noninverting and inverting terminals is negative or positive, respectively. We will first assume that resistor R.sub.3 is grounded so that no input signal V.sub.i is applied to the amplifier. Assume further that we are at a point in time where the output voltage V.sub.o is at +10 volts. At this point, capacitor C.sub.1 is being charged through negative feedback resistor R.sub.f toward the positive output voltage. The charging of capacitor C.sub.1 takes place with a time constant approximately equal to R.sub.f C.sub.1 since R.sub.3 is made very large. Now assume that R.sub.1 and R.sub.2 equal 1K and 9K, respectively, so that the voltage present at the noninverting U1 input is 1 volt. This means that as soon as capacitor C.sub.1 is charged to 1 volt, the comparator switches states which causes the output voltage to go to -10 volts. At this point, capacitor C.sub.1 begins to discharge from its +1 volt level toward the negative output voltage through resistor R.sub.f. The noninverting input terminal voltage V.sub.p immediately goes to -1 volt. The output V.sub.o then remains at -10 v until capacitor C.sub.1 has discharged to approximately -1 volts, at which point comparator U1 again switches state causing V.sub.o to go to +10 v. The cycle then repeats as before.
The amplitudes of the voltages V.sub.o and V.sub.c are both shown plotted against time t in FIGS. 2a and 2b. V.sub.o is seen to be a square wave form oscillating between +10 and -10 volts. V.sub.c, on the other hand, is a triangular waveform oscillating between +1 and -1 volts which represents the charging and discharging of capacitor C.sub.1. (It is assumed that the frequency at which C.sub.1 charges and discharges is high enough to be essentially linear.) What has been described, therefore, is a square wave oscillator. The edge transitions of V.sub.o coincide with the positive and negative peaks of V.sub.c. It should be apparent that the time between edge transitions of V.sub.o depends upon how long capacitor C.sub.1 takes to charge to its negative or positive peak value. That, of course, depends upon the RC time constant (i.e., on the value of R.sub.f C.sub.1) and on the magnitude of the peak charging voltages. The latter depends upon the value of R.sub.2 since it, combined with R.sub.1, forms a voltage divider to feed back a portion of the output to the noninverting input of U1 where it is compared by U1 to the voltage of its inverting input. If R.sub.2 is made larger with respect to R.sub.1, less voltage is fed back which means that V.sub.c will make smaller voltage swings in causing comparator U1 to change state. If the time constant R.sub.f C.sub.1 is unchanged, the frequency of both V.sub.c and V.sub.o will therefore be increased as R.sub.2 is made larger. In an extreme case where R.sub.2 is made infinite, (i.e., an open circuit) the oscillator frequency becomes theoretically infinite since capacitor C.sub.1 never has a chance to charge or discharge before comparator U1 changes state. Resistor R.sub.2 thus enables a workable oscillator by providing a kind of hysteresis to the circuit so that capacitor C.sub.1 is given some time in which to charge or discharge.
Now assume that a positive D.C. voltage V.sub.i is applied through resistor R.sub.3 to capacitor C.sub.1. Capacitor C.sub.1 presents an open circuit to a D.C. signal so the circuit operates as a conventional operational amplifier. Therefore, V.sub.i is inverted and amplified by the ratio of R.sub.f to R.sub.3 and appears as a negative D.C. signal in the output V.sub.o. However, since neither the amplitude nor the fundamental frequency of V.sub.o can change due to the inherent characteristics of the circuit, the only way the negative D.C. component can manifest itself at the output is for the width of the positive pulses to decrease while that of the negative pulses increases. The result is a waveform with the same fundamental frequency but with a negative D.C component equal to V.sub.i multiplied by the ratio of R.sub.f to R.sub.i. The additional D.C component of V.sub.o also changes V.sub.c since capacitor C.sub.1 will take a little more time to charge and a little less time to discharge. The positive D.C. signal V.sub. i charges capacitor C.sub.1 positively which adds to the cyclical charging and discharging of C.sub.1 as described above in a manner which increases the discharging time and decreases the charging time. FIG. 3b shows the resulting V.sub.c waveform where the slopes of the waveform's positive going excursions are steeper while the negative going excursions are flattened as compared with the V.sub.c waveform in FIG. 2a. FIG. 3a shows the corresponding V.sub.o waveform where the positive pulses are narrowed while the time between positive pulses is increased. The fundamental frequency of V.sub.o is unchanged though, because however much the charging time of capacitor C.sub.1 is decreased, the discharging time is increased by the same amount.
Exactly the same situation as described above occurs if the signal V.sub.i is a negative D.C. voltage with the positive pulses of V.sub.o being widened instead of narrowed. The circuit operates similarly with a continuously varying V.sub.i signal as long as the highest frequency component of V.sub.i is small as compared to the fundamental oscillator frequency of V.sub.o. The result is that the V.sub.o waveform is pulse-width modulated by an amplified V.sub.i signal. The V.sub.i signal can be recovered by passing V.sub.o through an appropriate low pass filter LPF to give the amplified output signal V.sub.f.
What has been described above is sometimes called a hysteretic switching amplifier, referring to the hysteresis provided by the positive feedback resistor R.sub.3. The aforementioned advantages of insensitivity to component characteristics and high efficiency are obtained with such an amplifier. One problem which is inherent to the amplifier circuitry, however, is the uncertainty existing as to exactly when the comparator U1 changes state. That is, when V.sub.c equals V.sub.p. Comparator U1 is then in an indefinite state and one cannot exactly predict when it will respond and switch states. This uncertainty manifests itself as noise in the output of the amplifier after V.sub.o is passed through a low pass filter.